Answers
Answer:
4, 12, 44, and 173.
Explanation:
Given the recursion formula:
[tex]\begin{gathered} a_n=4a_{n-1}-4 \\ a_1=4,n\geqslant2 \end{gathered}[/tex]We want to find the first four terms of the sequence.
[tex]\begin{gathered} a_2=4a_{2-1}-4=4a_1-4=4(4)-4=16-4=12 \\ \implies a_2=12 \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} a_3=4a_{3-1}-4=4a_2-4=4(12)-4=48-4=44 \\ \implies a_3=44 \end{gathered}[/tex]Finally:
[tex]\begin{gathered} a_4=4a_{4-1}-4=4a_3-4=4(44)-4=176-4=173 \\ \implies a_4=173 \end{gathered}[/tex]The first four terms of the sequence are 4, 12, 44, and 173.
Related Questions
Find the distance of a wheel where the radius is 10 feet and it gives 15 rotations. How many inches did the wheel travel in those 15 rotations?
Answers
We will find the distance after 15 rotations by multiplying the perimeter of the circumference by 15, that is:
[tex]d=15(2\pi r)\Rightarrow d=30\pi(10)\Rightarrow d=300\pi\Rightarrow d\approx941.48[/tex]From this, we have that the wheel traveled approximately 941.48 feet.
Max exercise 4 hrs during each 7 day week. At this rate, how many hours do he exercise in 35 days?
Answers
We know that Max exercises 4 hours during each 7-day-week.
After 35 days (5 weeks), the number of hours would be
[tex]4\cdot5=20[/tex]Max would exercise 20 hours after 35 days.Which integer represents this scenario? a fish grows 4 inches a) -4" b) 4” 6.NS.5
Answers
as it is about growth, the integer is positive, therefore
answer is b) 4"
450 students are graduating. 68% are going to college. 14% are working. How many students are unsure about what to do?
Answers
ANSWER
81 students
EXPLANATION
We have that 450 students are graduating.
68% (out of 100%) are going to college while 14% (out of 100%) are working.
To find the percentage of the studetns that are unsure about what to do, we have to subtract the percentages of those that know what to do from 100%.
That is:
100 - (68 + 14)
=> 100 - 82
=> 18%
Therefore, 18% of people are unsure about what to do.
Now, to find the number of students, we multiply this percent by the total number of students (450):
[tex]\begin{gathered} \frac{18}{100}\cdot450 \\ =\text{ 81} \end{gathered}[/tex]81 students are unsure about what to do.
which of the following equations is a direct variation equation that has the ordered pairs 12.5, 5 as a solutiona. y=7.5xb. y=x-7.5c. x=y+7.5d. y=2.5x e. y= -2.5x f. (2/5)x
Answers
The ordered pair given is 12.5, 5
This means that
When x = 12.5, y = 5
Looking at the given equations, if we substitute the values of x and y, the correct option would be C
The equation is expressed as
x = y + 7.5
By substituting, it becomes
12.5 = 5 + 7.5
12.5 = 12.5
The correct option is C
Generalize Two data sets have the same number of values. The first data set has a mean of 7.2 and a standard deviation of 1.25. The second data set has a mean of 7.2 and a standard deviation of 2.5. Which data set is more spread out?
Answers
ANSWER
The second data set is more spread out
EXPLANATION
The standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.
In this problem, the second data set has twice the standard deviation of the first data set, so it's more spread out.
Find the absolute value of | 2x+ z | + 2y x = 2.1, y = 3, z = -4.2
Answers
6
Explanations:The given absolute value expression is:
| 2x+ z | + 2ySubstitute x = 2.1, y = 3, z = -4.2 into the given expression:
[tex]|2(2.1)+(-4.2)|+2(3)[/tex]This can be simplifed as:
[tex]|2(2.1)-4.2|+6[/tex][tex]|4.2-4.2|+6[/tex]Since |4.2-4.2| = 0, the expression above becomes:
0 + 6
= 6
Therefore, the absolute value of the expression, after simplification, is 6
Using the graph of f(x)=x^2 as a guide describe the transformations and then sketch a graph of each function g(x)=(x-5)^2
Answers
1) In comparison to that parent function y =x², in g(x) = (x-5)² we have a horizontal translation to the right. in 5 units.
2) As we can see below:
Note that the Potting tool expands the (x-5)².
Suppose that you want to buy 6 different books and the order that you buy them does not matter. Then thenumber of ways to choose 6 books from 44 available books is
Answers
We have that the order doesn't matter without repetition, so should use combinations that are represented by the next formula:
[tex]C=\frac{n!}{r!(n-r)!}[/tex]Where n is the total of books and r the numbers of the group, in this case, 6 differents books.
Replace these values:
[tex]\frac{44!}{6!(44-6)!}[/tex][tex]C=\frac{44!}{6!(38)!}=7059052\text{ ways to choose 6 books from 44 available}[/tex]Math Lab A - Section 203B Notebook Home Insert Draw View Class Notebook U abe А. = = A Styles ☆ ? The table shows the average mass, in kilograms, of different sizes of cars and trucks. Size Small Car Average Mass (kilograms) 1,354 1,985 Large Car Large Truck 2,460 Part A To the nearest hundred, how much greater is the mass of a large truck than the mass of a small car? Fill in the blanks to answer the question. To the nearest hundred, a large truck has a mass of kilograms, and a small car has a mass of kilograms. So, a large truck has a mass about kilograms greater than a small car.
Answers
Given:
Round the mass of the large car to the nearest thousand.
Because 1985 is between 1,000 and 2,000 and closer to 2,000 ,the number should round up to 2,000.
Option D is the correct answer.
simplify the expression tan (3 x+ 2pi) as the tangent of a single angle
Answers
tan(3x)
Explanation
[tex]\tan (3x+2\pi)[/tex]Step 1
remember some property
[tex]\tan (a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b}[/tex]then
[tex]\begin{gathered} \tan (3x+2\pi)=\frac{\tan 3x+\tan 2\pi}{1-\tan 3x\tan 2\pi}\text{ Equation(1)} \\ \tan \text{ 2}\pi=0 \\ so \\ \tan (3x+2\pi)=\frac{\tan 3x+0}{1-\tan 3x\cdot0}\text{ } \\ \tan (3x+2\pi)=\frac{\tan \text{ 3x}}{1-0}=\frac{\tan \text{ 3x}}{1} \\ \tan (3x+2\pi)=\tan (3x) \end{gathered}[/tex]I hope this helps you
What is the solution to 4x+6. A x<3 B x<6 C x<48 D x<96
Answers
we have the inequality
[tex]4x+6\leq18[/tex]solve for x
subtract 6 both sides
[tex]\begin{gathered} 4x\leq18-6 \\ 4x\leq12 \end{gathered}[/tex]step 2
Divide by 4 both sides
[tex]x\leq3[/tex]If f(5)=3, write an ordered pair that must be on the graph of y = f(x + 1) + 2
Answers
(4, 5)
Explanations:The given function is:
y = f(x + 1) + 2
There are many ordered pairs that can be on the graph of y = f(x + 1) + 2, but with the information given will can look for one of them.
Let x = 4
y = f(x + 1) + 2
y = f(4 + 1) + 2
y = f(5) + 2
Since it is given that f(5) = 3, the equation above can be simplified to get the value of y.
y = f(5) + 2
y = 3 + 2
y = 5
Therefore, an ordered pair that must be on the graph of y = f(x+1) + 2 is (4, 5)
Mary is 4 years older than Sue. If the sum of their ages is 16. How would you set up the equations?
Answers
Answer:
A. x=y-4, x+y=16
C. x=y-4, x+y=16
Explanation:
• Let Sue's age = x
Mary is 4 years older than Sue, therefore:
• Mary's age, y = x+4
[tex]\begin{gathered} y=x+4 \\ \implies x=y-4 \end{gathered}[/tex]Next, the sum of their ages is 16. This gives:
[tex]x+y=16[/tex]Therefore, the equation is:
[tex]\begin{gathered} x=y-4 \\ x+y=16 \end{gathered}[/tex]The correct choices are A and C.
I need help with this trigonometric function I will upload a photo
Answers
For us to be able to determine the distance along an arc on the surface of the earth, we will be using the following formula:
[tex]\text{ S = r}\theta[/tex]Where,
S = arc length
r = radius (radius of the earth)
θ = central angle (in radian)
Given:
r = 3960 miles
θ = 48 mins.
a.) Let's convert the given measure of the central angle to radian.
[tex]\theta=48mins.\text{ = (48 mins.) x }\frac{1^{\circ}}{(60\text{ mins.})}\text{ = }\frac{48}{60}(1^{\circ})[/tex][tex]\theta\text{ = }\frac{4}{5}^{\circ}[/tex][tex]\text{ }\theta_{radian}\text{ = }\theta_{degrees}\text{ x }\frac{\pi}{180^{\circ}}[/tex][tex]\text{ }\theta_{radian}\text{ = }\frac{4}{5}\text{ x }\frac{\pi}{180}\text{ = }\frac{4\pi}{900}\text{ = }\frac{\pi}{225}\text{ radians}[/tex]b.) Let's now determine the distance (arc length).
[tex]\text{ S = r}\theta[/tex][tex]\text{ S = (3960)(}\frac{\pi}{225}\text{ ) = }\frac{3960\pi}{225}\text{ miles = 17.6}\pi\text{ miles = 55.2920307 }\approx\text{ 55.292 miles}[/tex]Therefore, the answer is 55.292 miles.
The graph below shows the relationship between the amount of time a ferris wheel has been moving and the height above ground of a seat on the ferris wheel. based on the graph. Which statement best describes why height is a function of time in the relationship?
Answers
ANSWER
b. Each value of time has exactly 1 value for height associated with it.
EXPLANATION
A function is a relationship where each value of the function has only one value of the variable associated with that value. In this problem, the function is height and the variable is time, therefore the answer is option b.
A farmer has 1,416 feet of fencing available to enclose a rectangle area bordering a river. No fencing is required along the river. Let x represent the length of the side of the rectangular enclosure that is perpendicular A(x)= Find the dimensions that will maximize the area. The length of the side rectangle perpendicular to the river is and the length of the side of the rectangle parallel to the river is.What is the maximum area?
Answers
The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 250632 ft²
Explanation:Given:
The length of the fencing = 1416 ft
The length of the side rectangle perpendicular to the river = x
To find:
The dimensions that will maximize the area
To determine the dimensions, we will make an illustration of the given information:
let the length o the rectangle parallel to the river = y
Length of the for the enclosed area = Perimeter of the enclosed area
Perimeter of the enclosed area = x + x = y = 2x + y
[tex]1416=2x+y\text{ . . .\lparen1\rparen}[/tex]Area of the rectangle = length × width
length = y, width = x
let the Area of the rectangle = A(x)
[tex]A(x)\text{ = xy . . . \lparen2\rparen}[/tex]To get the expression for A(x), we will make y the subject of the formula in equation (1):
y = 1416 - 2x
substitute for y in equation (2):
[tex]\begin{gathered} A(x)\text{ = x\lparen1416 - 2x\rparen} \\ \\ A(x)\text{ = 14166x - 2x}^2 \end{gathered}[/tex]To get the maximum dimension, we will differentiate with respect to x:
[tex]\begin{gathered} A^{\prime}(x)\text{ = 1416 - 4x} \\ \\ At\text{ maximum, A'\lparen x\rparen = 0:} \\ 1416\text{ - 4x = 0} \\ 1416\text{ = 4x} \\ x\text{ = }\frac{1416}{4} \\ x\text{ = 354} \end{gathered}[/tex]substitute for x in equation (1):
[tex]\begin{gathered} 1416\text{ = 2\lparen354\rparen + y} \\ 1416\text{ - 708 = y} \\ y\text{ = 708} \end{gathered}[/tex]The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 354 × 708
The maximum area = 250632 ft²
The United States Pentagon building is modeled on the coordinate plane as regular pentagon ABThe vertices of the pentagon are A(-7.42,2.42), B(0,7.88),C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35) what is the approximate perimeter in feet of the us pentagon building
Answers
Given,
The coordinates of the vertices of the pentagon is,
A(-7.42,2.42), B(0,7.88), C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35)
Required
The approximate perimeter of the pentagon.
The perimeter of the pentagon is calculated as,
The length of side AB is,
[tex]AB=\sqrt{(-7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side BC is,
[tex]AB=\sqrt{(7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side CD is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The length of DE is,
[tex]DE=9.21[/tex]The length of AE is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The perimeter of the pentagon is,
[tex]Perimeter=9.2124+9.2124+9.211+9.211+9.21=46.0568[/tex]Hence, the perimeter of the pantagon is 46.0568.
[tex]y = \frac{1}{3} x + 15[/tex]what is the answer
Answers
The slope of the given equation is ,
[tex]m=\frac{1}{3}[/tex]Slope of perellel line will also be same = 1/3 ,
The equation of perellel line is ,
[tex]\begin{gathered} y-0=\frac{1}{3}(x-6) \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]The formula is A=P(1+r/n)^nt8. Oswald Chesterfield Cobblepot invests $5,000 into an account that earns 2.5% interestcompounded monthly.a. How much money is in the account after two years? Use the formula above.Answer:b. How much money in interest was earned?Answer:
Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given formula with definition of terms
Compounded Amount is gotten using:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]Where:
A =final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
STEP 2: Write the given parameters
[tex]P=5000,r=\frac{2.5}{100}=0.025,t=2,n=12\text{ since it is compounded monthly}[/tex]STEP 3: Calculate the Compounded Amount
[tex]\begin{gathered} A=5000(1+\frac{0.025}{12})^{2\times12} \\ A=5000(1+0.002083333333)^^{24} \\ A=5000\times1.0020833333^{24} \\ A=5000\times1.05121642 \\ A=5256.0821 \\ A\approx5256.08 \end{gathered}[/tex]STEP 4: Calculate the compounded interest
[tex]\begin{gathered} Interest=Amount-Principal \\ \text{By substitution,} \\ Interest=5256.08-5000 \\ Interest=256.08 \end{gathered}[/tex]Hence,
$5256.08 was in the account after 2 years
The interest earned was $256.08
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 7z
Answers
Answer:
(-3, 4)(5, 0)=====================
Given systemx + 2y = 5 x² + y² = 25Rearrange the first equationx = 5 - 2y Substitute the value of x into second equation(5 - 2y)² + y² = 254y² - 20y + 25 + y² = 255y² - 20y = 0y² - 4y = 0y(y - 4) = 0y = 0 and y = 4Find the value of xy = 0 ⇒ x = 5 - 2*0 = 5y = 4 ⇒ x = 5 - 2*4 = -3Answer:
[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\;x+2y=5\\x^2+y^2=25\end{cases}[/tex]
To solve by the method of substitution, rearrange the first equation to make x the subject:
[tex]\implies x=5-2y[/tex]
Substitute the found expression for x into the second equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}x=5-2y \implies (5-2y)^2+y^2&=25\\25-20y+4y^2+y^2&=25\\5y^2-20y+25&=25\\5y^2-20y&=0\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}5y^2-20y&=0\\5y(y-4)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for y:
[tex]5y=0 \implies y=0[/tex]
[tex]y-4=0 \implies y=4[/tex]
Substitute the found values of y into the first equation and solve for x:
[tex]\begin{aligned}y=0 \implies x+2(0)&=5\\x&=5\end{aligned}[/tex]
[tex]\begin{aligned}y=4 \implies x+2(4)&=5\\x+8&=5\\x&=-3\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
A pie shop bakes a certain amount of pies each week. 150 of those pies are apple pies. These apple pies makes up 40 percent of the total pies. How many pies does the shop make each week?
Answers
The number of apple pies made each week is 375
Here, we want to know the total number of pies made per week
Let the total number of pies be p
From the question, 40% of p is 150
Thus, we have it that;
[tex]\begin{gathered} 40\text{ \% of p = 150 } \\ \frac{40}{100}\times\text{ p = 150} \\ 40p\text{ = 100}\times150 \\ \\ p\text{ = }\frac{100\times150}{40} \\ p\text{ = 375} \end{gathered}[/tex]Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.Interval notation for the above graph in inequality is______
Answers
Answer:
[tex](-∞,4)[/tex]Step-by-step explanation:
To solve the following inequality, use inverse operations.
[tex]\begin{gathered} -8x-4>-36 \\ -8x>-32 \\ x<\frac{-32}{-8} \\ x<4 \\ \text{ Interval notation:} \\ (-∞,4) \end{gathered}[/tex]Now, for the number line representing this inequality:
The square of the difference between a number n and eighty
Answers
Given the statement: The square of the difference between a number n and eighty.
we need to write the algebraic expression for the statement.
The difference between the number n and 80 will be:
[tex]n-80[/tex]The square of the difference will be:
[tex](n-80)^2[/tex]In the front of a building there are three doors each to be painted
a different color from 10 different available colors. How many color
arrangements for the doors are there?
Answers
In this case, the order doesn't matter and the colors cant be repeated.
Now, we need to use the permutation formula:
[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]Where n represents the total different available colors and r is equal to
the number of doors.
Replacing on the permutation formula:
[tex]P(10,3)=\frac{10!}{(10-3)!}[/tex][tex]P(10,3)=\frac{10!}{7!}[/tex][tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=10x9x8![/tex]Then
[tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=720[/tex]Hence, there are 720 possible arrangements for the doors.
Hello! I need help in answering question number 3 which I will attach. Geometry 3 D shapes. It reads To make one order you need to fill the cone with ice cream first, and then add the scoop on top. How many total cubic inches of ice cream are in one order?
Answers
The ice-cream is made up of of a sugar cone and a scoop in the shape of half a sphere
Hence, the formula for the volume V of the total cubic inches of ice cream is:
[tex]\begin{gathered} V\text{ = Volume of cone + half a volume of a sphere} \\ V\text{ = }\frac{1}{3}\pi r^2h\text{ + }\frac{2}{3}\pi r^3 \end{gathered}[/tex]Given:
height of cone = 4.6 inches
radius of cone = 1.7 inches
radius of sphere = 1.7 inches
Substituting the given values:
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^2\text{ }\times\text{ 4.6 + }\frac{2}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^3 \\ =\text{ 24.211 in}^3 \\ \approx\text{ 24.21 in}^3 \end{gathered}[/tex]Answer:
24.21 cubic inches
Can you show me how to solve this and graph?
Answers
The points (x,y) whose values satisfy the equation -5y=13 belong to the graph of that equation.
First, isolate y by dividing both sides of the equation by -5 and simplifying:
[tex]\begin{gathered} -5y=13 \\ \Rightarrow\frac{-5y}{-5}=\frac{13}{-5} \\ \Rightarrow y=-\frac{13}{5} \end{gathered}[/tex]Then, the points (x,y) belon to the graph of the equation -5y=13 whenever the value of y is -13/5, regardless of the value of x. Then, choose two different values of x to find two points that belong to the graph. For example, x=0 and x=2. Then, this two points belong to the graph:
[tex]\begin{gathered} (0,-\frac{13}{5}) \\ (2,-\frac{13}{5}) \end{gathered}[/tex]Notice that -13/5=-2.6,
Plot the points (0,-2.6) and (2,-2.6) in a coordinate plane:
Since the given equation is linear, the graph of the equation is a straight line. We can draw a straight line between any two points given. Draw a line between (0,-2.6) and (2,-2.6) to find the graph of the equation -5y=13:
Pleasr help fast it's due today 1. Consider the surface area of the following pyramid.224 am4 am4 am2.24 cm4 cm3 cm4 cm4 cm3 cm13 cm4 cm4 cm3 cm4 cm4 cm3 cm(a) Calculate the total surface area of the pyramid. Show your work.
Answers
Given data:
The given figure of square pyramid.
The expresssion for the total surface area is,
[tex]\begin{gathered} \text{TSA}=(3\text{ cm)(3 cm)+4}\times\frac{1}{2}(3\text{ cm)(}2.24\text{ cm)} \\ =9cm^2+2(3\text{ cm)(2.24 cm)} \\ =22.44cm^2 \end{gathered}[/tex]Thus, the total surface area of the given pyramid is 22.44 sq-cm.
2/7 in reduced terms
Answers
2/7 is in reduced terms already
no simplification can be made over this fraction.
hope it is clear
by noon the temperature in Buffalo had risen to 18 degrees farenheit what was the temperature there at noon Buffalo is a - 9
Answers
If the temperature of buffalo rised 18 degrees means that it is an addition between the 2 temperatures
[tex]-9+18=9[/tex]the temperature at noon is 9°F